What is the point of Blenders camera sensor width?
Cameras in Blender are made to resemble cameras in real world. The size of the sensor is important when you need to match content created with a real camera with your CG, and that happens really often. Obviously, you might have a hard time to match your camera if you don't enter the correct sensor size. You should search for it online for the specific camera model your content is captured with. 

You may also be used to real world cameras so it is easier to reach some desired result if you already know what to expect from some settings or parameters because they match real cameras. 

If you have a look, you can see that Blender even comes with lot of presets matching real cameras: